May I omit the definite article here? Or else it'll be 'the The'

Question

The name of the popular daily is The New York Times. I'm talking about its reporter. May I omit the definite article from this sentence?

I'm talking about Paul, the The New York Times reporter.

The first the is grammatically introduced as a modifier of the word reporter whereas the capital The is the part of the daily's name.

Is this right then?

I'm talking about Paul, the New York Times reporter.

I must include the (and not The) in my sentence.

Answer 1

Yes, this "the" is regularly omitted, and the capital "The" in the second sentence would be wrong (because "the" is modifying "reporter," not "New York Times").

Answer 2

I'm talking about Paul, the New York Times reporter. is incorrect because "The New York Times" is itself the name of newspaper. So writing "I'm talking about Paul, The New York Times reporter" will be good enough for you :)